5. Given the observations 45, 20, 30, and 25, the mean absolute deviation is clo

Question

5. Given the observations 45, 20, 30, and 25, the mean absolute deviation is closest to A. 4.0 B. 7.5 C. 8.3 6. Adam Farman has been asked to estimate the volatility of a technology stock index. He has identified a statistic which has an expected value equal to the population volatility and has determined that increasing his sample size will decrease the sampling error for this statistic. Based only on these properties, his statistic can best be described as: A. unbiased and efficient. B. unbiased and C. efficient and consistent. consistent. 7. According to Chebyshev's inequality, the minimum proportion of observations falling within three standard deviations of the mean for a negatively skewed distribution is closest to A. 8990. B. 72%. C. 65%. 8. A researcher has investigated the returns over the last five years to a long-short strategy based on mean reversion in equity returns volatility. His hypothesis test led to rejection of the hypothesis that abnormal (risk-adjusted) returns to the strategy over the period were less than or equal to zero at the 1% level of significance. He would most appropriately decide that: A. his firm should employ the strategy for client accounts because the abnormal returns are positive and statistically significant. B. while the abnormal returns are highly significant statistically, they may not be economically meaningful. C. as long as the estimated statistical returns are greater than the transactions costs of the strategy, his firm should employ the strategy for client accounts.

Explanation / Answer

1. Mean = (45+20+30+25) / 4 = 30.

MAD = (|45-30| + |20-30| + |30-30| + |25-30|) / 4 = 30/4 = 7.5.

The mean absolute deviation is 7.5, hence the option is B.

2. An unbiased estimator has an expected value equal to the true value of the population parameter. A consistent estimator is more accurate the greater the sample size. An efficient estimator has a variance of sampling distribution that is less than that of any other unbiased estimator. Hence the correct option is B.

3. According to Chebyshev’s inequality, the proportion of the observations within 3, which gives k = 3, standard deviations of the mean is at least

= 1 - (1/k^2) = 1 - (1 / 3^2)

= 0.89 or 89%.

Hence the correct option is A.

4. The correct option is B.

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